"Common Space" DW-NOMINATE Scores With Bootstrapped
Standard Errors

This is the fourth release of Common Space DW-NOMINATE scores for the House and
Senate. The House and Senate were scaled as if they were one legislature using the
642 Legislators who served in both
the House and Senate as "glue" (bridge observations). That is, we estimated
a single ideal point for each member of Congress based upon his/her entire record of service
in Congress. In the Poole-Rosenthal framework we used the Constant model so that
each unique legislator has the same ideal point throughout his or her career. After the download
links we show some comparisons of these Common Space scores with our regular
DW-NOMINATE Scores for the House and Senate.

These new scores
for the 1st to the 112th Congresses
(1789 - 2012) contain parametric bootstrapped standard errors.
For an explanation
of the basic theory of the parametric bootstrap see:

This research was made possible by NSF Grant 0611880 to
Jeffrey B. Lewis,
Keith T. Poole, and
Howard Rosenthal.
This work was also supported in part by the Rice Terascale Cluster funded by NSF
under Grant EIA-0216467, and a partnership between Rice University, Intel,
and HP.
We thank the
National Science Foundation and the San Diego Supercomputer Center for their support.

There were a total of 100,947 roll calls of which 90,609 were scalable. The number of
unique legislators was 11,883 producing a total of 16,501,617 choices.
In the scaling, the second dimension weight is 0.4438 and the Beta
parameter (proportional to 1/s where
s is the standard deviation of the
error) is 7.0795. The correct classification is 87.06 percent with an
APRE of 0.6152 and a geometric mean probability of 0.7509.

In order to calculate distances
from these Common Space DW-NOMINATE scores you must multiply the
second dimension by the weight parameter. To calculate the choice
probabilities you must apply both the second dimension weight and
the Beta parameter. Use the Yea and Nay outcome coordinates
with considerable caution because, as we explain in Congress: A Political Economic History
of Roll Call Voting, they
are poorly identified. However, the cutting line is identified and
can be used safely.

Please note that these files contain scores for most Presidents.
For Presidents prior to Eisenhower these are based on roll calls corresponding
to Presidential requests. These roll calls were compiled by an NSF project
headed by Elaine Swift
(
Study No. 3371, Database of Congressional Historical Statistics, 1789-1989).
Many of these scores are based upon a small number
of roll calls so use them with caution!

A Comparison of the "Common Space" DW-NOMINATE Scores
With the Separate House and Senate 2-Dimensional Linear DW-NOMINATE Scores

The Joint Scaling of the House and Senate utilizes the 2-dimensional constant
model developed by Poole and Rosenthal in which each legislator has a single ideal point
throughout his or her career. In contrast, the standard DW-NOMINATE scores use the
2-dimensional linear model in which a legislator is allowed to move on
a straight line throughout his or her career. These models are discussed in detail in:

Keith T. Poole and Howard Rosenthal. 1997. Congress: A Political-Economic History of
Roll Call Voting. New York: Oxford University Press.

The fit of the Joint Scaling is a half percentage point below the House fit but better
than the Senate fit. This reflects the fact that the House fit is better than the
Senate fit and the number of unique members in the House is more than five times the number
of unique members of the Senate. Consequently, when the chambers are combined it is not
surprising that the larger number of House members -- even with the constraint of the
constant model -- will drive the fit.

Below is a graph of the correct classifications for these three scalings. The pattern of
the classifications is essentially the same as that shown in Figure 3.1 of Ideology and
Congress. The correct classification of the joint scaling closely tracks that for
the separate House DW-NOMINATE scaling. The Pearson correlation between the two is 0.989.
The corresponding correlation between the joint scaling and the separate Senate DW-NOMINATE
scaling is 0.810. However, the correlation between the correct classifications for
the Senates within the joint scaling and the separate Senate DW-NOMINATE scaling
is 0.850. The corresponding correlation between the correct classifications
for the Houses within the joint scaling and the separate House DW-NOMINATE
scaling is 0.955.
What these correlations show is that, although constraining the members of Congress to
having a single ideal point throughout their careers, the patterns of overall
chamber classifications are almost exactly reproduced even though on average the classifications
of the joint model are lower.

Below is a graph of the polarization of the House and Senate since the end of Reconstruction (1879-2012)
using the joint space coordinates.
Polarization is measured as the distance between the two major parties on the first, liberal-conservative
dimension (see graph below). The pattern of polarization within the two chambers is almost the same with the
112th House being the most polarized chamber since the end of Reconstruction.

The three figures below show the Party Means for the current Post-Reconstruction
Democrat-Republican two-party system. The figures pretty much speak for themselves.
We have color coded the party lines and report correlations between the Party Means
from the joint scaling versus the separate scalings. Note that for the graphs of the
second dimension Party Means we separate out the Northern and Southern Democrats. The
basic message of these graphs is that the Joint scaling is reproducing the Party trend lines
during the whole Post-Reconstruction period.

Below is a QuickTime Movie of the Separate Scaling Results. The
Similarities discussed above can be clearly seen by studying this movie. Note
that the second dimension is shown with the proper weighting.